Resistance of a wire on stretching
(a) increases n2 times original resistance if length is increased n times.
(b) decreases n4 times if the radius of a wire is increased n times.
Provided mass, density & resitivity wire are kept fixed.
Ohm’s law
(a) 
= constant called electrical resistance R, provided there is no change in the physical conditions like temperature, pressure & impurity etc.
(b) 
= (Microscopic version) i.e. conductivity of a conductor is independent of electric field existing in the material over a wide range of field.
Resistivity of conductors (ρ)
Resistance per unit length per unit cross sectional area of a material is called its resistivity or specific resistance, for metals it is (a) 
.
Its reciprocal is called conductivity or specific conductance (σ). Both ρ & σ are independent of length, thickness, & shape or geometry.
Current mechanism in conductors
In metals about 10 29 m – 3 of free electrons (called average number density ‘n’ ) move randomly (disordered) in all directions (like motion of gas particles) with average thermal speed of about 105 m/s & collide randomly with the metal ions (almost fixed). Between the collision the free electrons travel along straight lines with average relaxation time (t) of about 10 – 14 s, however due to random motion net charge (electrons) crossing any imaginary plane is zero. On applying external potential difference across a metal an electric field is created in it, which exerts force on electron opposite to the direction of electric field & electron apart from thermal motion (disordered) now start drifting in a definite direction (opposite to the direction of electric field) . Using v – t eqn. the drift velocity of free electrons in metals is 
.
Average value of drift velocity of free electrons in metals is of the order of few mm /s. Drift velocity per unit applied electric field is called electron mobility (μ) i.e.
Let ‘n’ be the no. density (i.e. N/V) of free electrons of a metal, then current equation for metal slab of cross sectional area A is
1 A is the flow of 6.25 x 10 18 electrons per second.
Wheatstone bridge
The arrangement of five capacitors as shown is called Wheat stone bridge.
If 
then points P & Q are at same potential & the bridge is said to be balanced, due to this no charge will flow in the arm PQ & hence arm PQ can be removed & circuit can becomes as shown.
The effective capacitance across the points X & Y for the balanced state of Wheatstone bridge is 
the bridge is not balanced, then the problem can be solved using Kirchoff’s laws.
Series grouping of capacitors
1. Charge on all the components connected in series is same (i.e. q = constant).
2. Potential difference is divided among the various capacitors in accordance with 
e. a capacitor of smaller capacitance will get more potential difference & vice versa.
3. Effective capacitance is given by, 
Conduction
Suppose two charged metal spheres of radii R1 & R2 of different potentials are joined by a metal wire, then charge flows from conductor at higher potential to that at lower potential till both acquire the same potential ‘V’ called common potential. This stage is called steady state & is achieved almost immediately after joining the charged conductors.
1. Common potential at steady state can be calculated using charge conservation i.e. total charge of conductor 1 & 2 before joining
& after joining is same i.e.
q1bj + q2bj = C1 V + C2 V
Or V = V1 aj = V2 aj 
The above relation can be expressed as
2. Charge on each conductor after joining is
As q = C V & C ∝ R, thus bigger sphere gets more charge after conduction.
3. Total energy of the system before joining is
Total energy of the system after joining is
Uaj is found to be smaller than Ubj. The system looses some of its energy in the form of heat, which is given by
PPC with a dielectric slab in plates
If a dielectric slab of dielectric constant K, thickness t < d is placed between the plates of a PPC then due to the electric field 
between the capacitor plates the dielectric gets polarized & an electric 
is induced in it, as a consequence net electric field in dielectric is found to be 
.
Due to this field electric field net potential difference across the capacitor plates becomes 
.
Using C = q/V, capacitance of capacitor becomes 
.
1. If the entire space between the capacitor plates is occupied by air or vacuum, then 
. [using K = 1 and t = 0]
2. If the entire space between the capacitor plates is occupied by dielectric, then 
[using t = d]
If a physical quantity can be completely described by telling its magnitude only and direction is meaningless for it, then it is called a scalar.
*Dimensional Variables
Are the physical quantities which have dimensions as well as variable values.
e.g. Force, Mass, Velocity, Area, Volume etc.
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